Interdiscip Sci
. 2010 Sep;2(3):228-40. doi: 10.1007/s12539-010-0022-0. Epub 2010 Jul 25.
=[=Codon populations in single-stranded whole human genome DNA Are fractal and fine-tuned by the Golden Ratio 1.618==
Jean-Claude Perez 1
https://pubmed.ncbi.nlm.nih.gov/20658335/
Abstract
This new bioinformatics research bridges Genomics and Mathematics. We propose a universal "Fractal Genome Code Law": The frequency of each of the 64 codons across the entire human genome is controlled by the codon's position in the Universal Genetic Code table. We analyze the frequency of distribution of the 64 codons (codon usage) within single-stranded DNA sequences. Concatenating 24 Human chromosomes, we show that the entire human genome employs the well known universal genetic code table as a macro structural model. The position of each codon within this table precisely dictates its population. So the Universal Genetic Code Table not only maps codons to amino acids, but serves as a global checksum matrix. Frequencies of the 64 codons in the whole human genome scale are a self-similar fractal expansion of the universal genetic code. The original genetic code kernel governs not only the micro scale but the macro scale as well. Particularly, the 6 folding steps of codon populations modeled by the binary divisions of the "Dragon fractal paper folding curve" show evidence of 2 attractors. The numerical relationship between the attractors is derived from the Golden Ratio. We demonstrate that: (i) The whole Human Genome Structure uses the Universal Genetic Code Table as a tuning model. It predetermines global codons proportions and populations. The Universal Genetic Code Table governs both micro and macro behavior of the genome. (ii) We extend the Chargaff's second rule from the domain of single TCAG nucleotides to the larger domain of codon triplets. (iii) Codon frequencies in the human genome are clustered around 2 fractal-like attractors, strongly linked to the golden ratio 1.618.
https://link.springer.com/article/10.1007/s12539-010-0022-0
Published: 10 November 2007
Nucleotide Frequencies in Human Genome and Fibonacci Numbers
Michel E. Beleza Yamagishi & Alex Itiro Shimabukuro
Bulletin of Mathematical Biology volume 70, pages643–653 (2008)
Abstract
This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human single-stranded DNA and the famous Fibonacci’s numbers. The model relies on two assumptions. First, Chargaff’s second parity rule should be valid, and second, the nucleotide frequencies should approach limit values when the number of bases is sufficiently large. Under these two hypotheses, it is possible to predict the human nucleotide frequencies with accuracy. This result may be used as evidence to the Fibonacci string model that was proposed to the sequence growth of DNA repetitive sequences. It is noteworthy that the predicted values are solutions of an optimization problem, which is commonplace in many of nature’s phenomena.
https://link.springer.com/article/10.1007/s11538-007-9261-6